Strain-Rate Selection in the Constant-Rate-of-Strain Consolidation Test

Transcription

1 Research Report UKTRP-81-7 Strain-Rate Selection in the Constant-Rate-of-Strain Consolidation Test by C. Thomas Gorman Formerly Research Engineer Principal Kentucky Transportation Research Program College of Engineering Uniersity of Kentucky ln cooperation witb DEPARTMENT OF TRANSPORTATON Commonwealth of Kentucky and Federal Highway Administration U.S. DEPARTMENT OF TRANSPORTATON The contents of this report reflect the iews of the author who s responsible for the facts and the accuracy of the data presented herein, The contents do not necessarily reflect the official iews or policies of the Uniersity of KentuckY, of the Federal HighwaY Administration, or the Kentucky Department of Transportation. This report does not constitute a standard, specification, or regulation. June 1981

2 Tec'hnical Report Documentation Page 1. Report No. 2. Goernment Accession No. 3. Recip-ient's Catalog No. 4. Title and Subtitle 5. Report Date Strain-Rate Selection in the Constant-Rate-of-Strain Consolidation Test June Performing Organiation Code 7. Author( s) 8. Performing Organiation Report No. C. Thomas Gorman UKTRP-81-7, 9. Performing Organiation Nome and Address Transportation Research Program College of Engineering Uniersity of Kentucky Lexington Kentucky Sponsoring Agency Name and Address Kentucky Department of Transportation State Office Building Frankfort, Kentucky Work Unit No. {TRAJS) 11. Contract or Grant No. KYHPR Type of Report and Period Coered 14. nterhn Sponsoring Agency Code 15. Supplementary Notes Prepared in cooperation with the US Department of Transportation, Federal Highway Administration Study Title: Controlled Rate of Strain and Controlled Gradient Consolidation Testing 16. Abstract Constant-rate-of-strain (CRS) consolidation tests were performed on remolded kaolinite specimens. The effect of strain rate on CRS test data is shown. A relation between soil parameters and strain rate was deeloped and used to formulate a strain-rate selection procedure. The fmal selectlon procedure is based on liquid limit and initial degree of saturation of the specimen and is presented in graphical form. The procedure is applicable to all types of soils. 17. Key Words 18. Distribution Statement Consolidation Laboratory Tests Strain Rate Constant-Rate-of-Strain Kaolinite Remolded 19. Security CloSsif. {of this report) 2. Security Clossif. (of this page) 21. No. of Pages 22. Price Form DOT F Reproduction of co:npleted page authoried

3 Contents ntroduction. Page 1 Sample Preparation 1 Testing. Equipment. ProcedUre 2, 2 3 Discussion. Stress-Strain Data Cy-Data. Parameters Affecting ubla Deelopment of the Strain-Rate Selection Procedure Deelopment of the Relationship between r, Cy, and ub/o. Strain-Rate Selection Guidelines Conclusions 15 Summary 15 References 15

4 List of Figures Figure 1. Schematic of CRS Test Equipment Page 3 Figure 2. CRS Test Equipment 3 Figure 3. Load Press 4. Figure 4. ncremental-load Test Equipment. 5 Figure 5. Specimen Trimmer. 5 Figure 6. Data Acquisition System and Tape Dri e 5 Figure 7. Stress-Strain Data from CRS and ncremental-load Consolidation Tests on Vac-Aire Extruded Specimens 6 Figure 8. Mechanical Model of Consolidation 7 Figure 9. Cy Data from CRS and ncremental-load Consolidation Tests on Vac-Aire Extruded Specimens 8 Figure 1. Comparison of Stress-Strain Data and Cy Data from CRS Tests 8 Figure 11. Comparison of Cy from Linear and Nonlinear Theory. 9 Figure 12. ubla' ersus a' from CRS Tests on Vac-Aire Extruded Specimens 9 Figure 13. Results of CRS Tests on Partially-Saturated Kaolinite. 1 Figure 14. Relationship between Strain Rate and ubla from CRS Tests on Vac-Aire Extruded Specimens 11 Figure 15. Strain-Rate Selection Chart for Saturated Soils Based on Cy and ub/a 12 Figure 16. Strain-Rate Selection Criteria for Saturated Soils 13 Figure 17. Strain-Rate Selection Criteria Adjusted for Partially Saturated Soils 14 Figure 18. Relationship between nitial Degree of Saturation and Perpendicular Distance b etween Lines on the Strain-Rate Selection Chart 14 Figure 19. Strain-Rate Selection Chart 14

5 List of Tables Table 1. Engineering Properties of Kaolinite. Page 2 Table 2. Properties of Vac-Aire Extruded Specimens 2 Table 3. Properties of Mechanically Compacted Specimens 2 Table 4. Prediction of %fa for CRS Tests on Undisturbed Specimens Using Equation Table 5. Adjusted Strain Rates for Saturated Soils. 13

6 ntroduction The constant-rate-of-strain (CRS) consolidation test was introduced in 1959 (); the theory for complete reduction of data was deeloped in 1971 (2). n 1976 (3), the CRS test was compared with the controlled-gradient and incremental-load consolidation tests. The 1976 report related the conclusion that the CRS test offers seeral adantages oer other methods of consolidation testing. The CRS test requires the least time to complete, is the least difficult to perform, and does not require sophisticated equipment. A disadantage is selecting a suitable strain rate which must be set prior to loading the soil specimen. Preious experimental research and theoretical deelopments (2, 4) hae shown that the magnitude of pore pressure deeloped at the base of the specimen, u b, must be maintained within certain limits to produce meaningful data. The alue of u b may be raised or lowered by increasing or decreasing the strain rate. Specifically, the limits on u b hae been based on the total ertical stress, a, by limiting u b. Guidelines for selecting approximate strain-rates were gien in the 1976 report (3) and were based on limited data then aailable. More specific guidelines are needed to fully deelop a standard method of test and to implement the test on a routine basis. This report refmes and extends the strain-rate selection guidelines. Strain-rate selection is not an exact procedure. The usefulness of the data does not depend on a precise selection of strain rate. Engineering judgment and the guidelines presented herein are sufficient to select a strain rate inasmuch as a wide range of acceptable rates exist for a gien soil. Engineering judgment must be based on a knowledge of the effects that different strain rates hae on the parameters determined in the CRS test and used in settlement analyses -- more specifically, the effect of strain rate on the coefficient of consolidation, C, apparent preconsolidation pressure, P C ' and compression ratio, CR. Deelopment of guidelines was based on a testing program using remolded kaolinite soil samples. A series of tests was performed to defme the effect of strain rate on results for gien soil conditions. The steps are outlined below: () The effect of different strain rates is discussed and the connection between these effects and u b is established. (2) The soil parameters that primarily affect u b for a gien strain rate are defined and discussed. The primary parameters are C and initial degree of saturation, S. (3) A relationship between strain rate and u b fa is established using test results obtained from CRS tests performed on the remolded kaolinite samples. (4) The relationship obtained from the remolded kaolinite test series is extended to ariable C and checked against CRS test data for other soils. (5) An upperbound is selected for allowable u b, thereby eliminating u b as a ariable in the rate selection criteria. The ariables in the rate selection criteria, at this point, are strain rate, r, and C. (6) A correlation between liquid limit and C is used as a basis for replacing C with liquid limit in the r-ersus-cy relation. (7) Test data obtained from CRS tests on partially-saturated kaolinite specimens are used to extend the r-ersus-liquid limit relationship and to deelop fmal strain-rate selection guidelines based on liquid limit and initial degree of saturation. Sample Preparation A kaolinite clay, obtained from the Edgar Kaolin Co., Edgar, Florida, was selected for the testing program. The index properties of this soil are shown in Table 1. Specimens were molded by two methods. The first method produced uniform samples, which were used to study strain-rate effects. A Vac-Aire extrusion machine produced solid cylindrical speci-

7 TABLE 1. Atterberg Limits Liquid Limit (Percent) Plastic Limit (Percent) ENGNEERNG PROPERTES OF KAOLNTE 59 Gradation Percent Silt 21 Percent Clay 79 Moisture-Density Relation Optimum Moisture (Percent) 35 Maximum Dry Density (kg/m 3 ) 132 (pet} 81.3 Classification Unified AASHTO Mineral Analysis Kaolinite (Percent) Quart (Percent) Talc (Percent) 34 MH A-7-5(36) mens 2.6 inches (66 mm) in diameter. The soil was mixed in a acuum hopper on!he machine and forced by augers ihrough a die of desired sie aud shape. The samples were cut into conenient lengths, waxed, and stored until testing. Properties achieed by this meihod are shown in Table 2. The second method of molding produced speci mens haing arious moisture contents to study the effect of initial degree of saturation. Compaction equipment is described in ASTM Standard Test Meihod for Moisture-Density Relations of Soils Using 5.5-lb. (2.5-kg) Rammer and 12-in. (34.8-mm) Drop, Designation D 698. These specimens were waxed and stored until testing. Properties obtained by this me!hod are shown in Table 3. TABLE 2. PROPERTES OF VA C-ARE EXTRUDED SPECMENS Moisture Content (Percent) Degree of Saturation (Percent) Dry Density (kg/m 3 ) (pet} Void Ratio i. l1 TABLE 3. PROPERTES OF MECHANCALLY COMPACTED SPECMENS Moisture Content (%) Degree of Saturation (%) Void Ratio (kg/m 3 ) Dry Density (pet} i.l i. l , , , , The first series of CRS tests were performed on uniform samples at 96 percent of saturation. All ariables were constant except for strain rate. Fie CRS tests were performed at fie strain rates. Two incre mental-load consolidation tests were also performed. The second series included tests on four partiallysaturated specimens, shown in Table 3, These specimens were tested at approximately the same strain rate. Some of!he equations deeloped in this report were compared wiih data obtained preiously (3). The tests were described in that report, and only pertinent data are presented here. 2 Testing EQUPMENT A schematic of the CRS equipment is shown in Figure. The equipment was designed in-house and fabricated by!he Machine Shop, Uniersity of Kentucky, College of Engineering. Seeral special features, Figure 2, are worihy of mention. The loading ram is guided into the chamber by a low-friction seal system described by Chan (5). The pressure trausducer to monitor pore-water pressure at the specimen base is mounted directly in the base plate. This reduces the flexibility of the pressure measuring system and reduces the time lag in pore-pressure measurement. The steel ring, to laterally confine the specimen, is sealed to

8 (a) (b) (c) (d) (e) (f) SPECMEN CONSOL DA TC N RNG CHAMBER POROUS STONE PORE-PRESSURE TRANSDUCER RESERVOR (g) DSPLACEMENT TRANSDUCER (h) LOADNG RAM ( i) BACK-PRESSURE REGULATOR ( j ) AR VENT.1- g) (h),tt t (i) l (;) / : (c) y, -,Ajfc!tlli 1/(aV/ Hb) ( t) l'<'.ig;y.. i Figure 1. Schematic of CRS Test Equipment. Figure 2. CRS Test Equipment. the chamber base plate by a flush -ring. The CRS consolidometer was loaded in a Karol Warner triaxial press. The adjustment of strain rate was by a gear reducer and ariable speed electric motor. They are shown in Figure 3. n addition to the CRS tests, two incrementalload consolidation tests were also performed. The Anteus back-pressure consolidometer shown in Figure 4 was used in these tests. PROCEDURE Each specimen was trimmed to 2.5 inches (64 mm) in diameter by 1. inch (25 mm) in height using the cutting shoe shown in Figure 5. The specimen was weighed and set in a stainless steel ring which confmed the specimen laterally. The ring and specimen were placed oer the bottom porous stone, and the ring was clamped to the chamber base. A porous stone and cap were placed on top of the specimen. After assembling the chamber, the ram was brought into contact with the cap. A linear ariable displacement transducer (LVDT) and strain-gage type transducer were installed. The chamber was filled with de-aired water. A back 3

9 Figure 3. Load Press. pressure of 1 psi (69 kpa) was applied to the top and bottom of the specimen. Swell was preented by the fixed ram. Approximately -15 hours after applying the back pressure, the drainage line to the bottom of the specimen was closed, and the specimen was loaded at a constant rate of strain. When a total ertical stress of approximately 3 tsf (3 MPa) was reached, the loading phase was stopped. The specimen was then unloaded at the same strain rate used in the loading phase. Pore-pressure transducer, load transducer, LVDT, and elapsed time readings were taken periodically by an automatic acquisition system and recorded onto magnetic tape for subsequent processing. The data acquisition system and tape drie are shown in Figure 6. Data reduction is shown in Equations 1 through 4: E Ll.H/H, r Ll.e/Ll.t, 2 a a - 2 u b /3, 3 c in which E Ll.H H o r Ll.e Ll.t a a u b strain, change in height from initial height, initial height, strain rate, change in strain in time interal Ll. t, time interal, ertical stress, effectie ertical stress, excess pore-water pressure deeloped at the base of the specimen, coefficient of consolidation, change in ertical stress in time interal Ll.t, and H H - Ll.H. The equation for C is based on the assumption that initial transient conditions, as described by W1ssa (2), hae dissipated. All alues of C reported herein were computed after u b reached a alue of.5 psi (3 kpa). 4 4

10 Figure 4. ncremental Load Test Equipment. Figure 6. Data Acquisition System and Tape Drie. Figure 5. Specimen Trimmer. Discussion STRESS STRAN DATA The results of fie CRS tests at arious strain rates and of two incremental load consolidation tests are shown in Figure 7. Strain for the incremental load tests were calculated from the deformation corre sponding to 1 percent hydrodynamic consolidation, according to ASTM Standard Method of Test for One Dimensional Consolidation Properties of Soils, Desig nation D 2435; and ail load increments were main tained for a 24 hour period. The shifting of stress strain cures in the direction of increasing stress at 5

11 VERTCAL EFFECTVE STRESS, u/ (MPa) 1 (TSF).5.1 "' <i a::.15 1-' (/).2.25 LEGEND TEST NO- STRAN RATE %/MN A X 9 72 <> NCREMENTAL 22 NCREMENTAL Pc TSF 1.5 1, MPa Figure 7. Stress-Strain Data from CRS and ncremental-load Consolidation Tests on Vac-Aire Extruded Specimens. higher strain rates is a well-documented phenomenon (, 4, 6, 7, 8). Such shifting suggests that primary and secondary consolidation do not occur at separate time interals during the consolidation process but, rather, occur simultaneously; and the amount of secondary consolidation is dependent on strain rate. t is important to note that this phenomenon is not unique to the CRS test but also occurs in incremental load tests. Crawford (6) noted this"... increasing contribution of secondary consolidation with long increments of loading..." in a series of incremental-load and CRS tests. Lowe (8) explained the phenomenon with a new, more realistic mechanical model in his modified Teraghi consolidation theory. The model is shown in Figure 8; his description of the model follows: "n the model for the Modified Theory, the coiled springs (Teraghi Model) are replaced with leaf springs haing a filling of iscous material between the leaes. The load these leaf springs can carry depends upon the rate of compression imposed. f the rate of compression imposed is ery fast, the iscous material between the leaes deelops appreciable shear resistance and the stack of leaes acts as a unit. f the rate of compression imposed is ery slow, the iscous filling material can deform readily and each of the leaes acts as an indiidual leaf. The resistance to compression when the stack of leaes acts as indiiduals is much less than the resistance when the stack acts as a combined beam as under the fast loading condition." Therefore, the effect of increasing strain rate on stress-strain data in the CRS test is not attributable to, or unique to, the CRS test itself. The effect is a result of the iscous nature of the particular soil being tested. The lower strain rates, which produce essentially the same stress-strain cures as incrementalwload testi; with 24-hour load-increments, are preferred in the deelopment of strain-rate selection criteria. The lower range of strain rates is preferred because the stress-strain 6

12 w alues of a ' all alues of C conerged. The alue of ' a at conergence also increased with increasing strain ' rate. This phenomenon is caused by two factors. The first is based on the decrease in permeability with decreasing oid ratio. As the sample is strained, the oid ratio decreases and permeability decreases; this tends to decrease C. Figure 1 illustrates this point at strain rates of.174 and.963 percent per minute., As the strain rate increases, strain, for a gien alue of: a ', decreases. Therefore, as the strain rate increases, C at the gien alue of ay' should increase. This is shown by the data only withiu a narrow range of a ' alues. For this reason, and because other factors obiously influence C, no attempt was made to quantify this trend. The second factor, which produces the rate effect shown in Figure 9, concerns the assumption of a stress-strain relationship for the material being tested. To obtain Equation 4, it was necessary to assume a linear stressstrain relation of the fonn 5 in which Aa ' ;; change in effectie ertical stress and m = coefficient of olume compressibility. Wissa (2) showed the consequences of an error in this assump tion by assuming a nonlinear stress-strain relation of the fonn = Ll.e/Ll.(log a ). 6 Substitution of this assumption for the linear stress strain assumption in the deriation of C yields H 2 log(a 2 ia l l + (2Ll.t log ( u b /ay)), 7 Figure 8. Mchanical Model of Consolidation (after Lowe (8)). in which a i and a 2 = total ertical stress at times t 1 and t, respectiely, and Ll.t = t 2 2 t 1. The relationship between the linear theory C and nonlinear theory C is expressed by combining Equations 4 and 7, yielding cur es seem less sensitie to strain rate in this range and because field conditions are more closely dupli cated by slower rates. 8 C DATA Values of C calculated from CRS test data were affected by strain rate. C 's for the CRS tests at different strain rates and for the incremental load tests are shown in Figure 9. A progressie increase in C was noted in the early portions of the CRS tests for pro gressiely increasing strain rates. Eentually, at higher The difference between the two solutions is solely a function of u / a and is expressed graphically in b Figure ; the solutions dierge as u /a increases. b The ariation of u /a throughout the CRS tests is b shown as a function of a ' in Figure 12. The quantity reaches a maximum early in the test and aries oer a wide range throughout the test. The way in which the 7

13 .., c:; "',.,. "'.,. ;!; "'' ' "1., LEGEND "' "! TEST NO. STRAN RATE Pc %/MN TSF MPo > u q "' "' X <> :::; c21 NCREMENTAL NCREMENTAL VJ., : u "- f- g Q w Q "- "- w "1' "' q u OO(TSF (MPol VERTCAL EFFECTVE STRESS, u/ Figure 9. C Data from CRS and ncremental Load Consolidation Tests on Vac-Aire Extruded Specimens f- VJ VERTCAL.4.6.l ::::...-._ "- EFFECTVE STRESS, U LEGEND (MPol 4 6 OO(TSF TEST NO. STRAN RATE ""' " %/MN "' -- " ' ' "-.... _ ' Figure 1. Comparison of Stress-Strain Data and Cy Data from CRS Tests "' <'!., "1 "" - g :g " "',. "' N N:i =,. > u ;:: "" :::; "' u u. f- "' u u. u. "' 8

14 stress-strain assumption, and hence the magnitude of u b ia, affect C is clearly shown in Figures and 12. These figures quantify the effect of an error in the stress-strain assumption and explain, phenomenon noted for the C data in Figure 9. in part, the The obious solution to this problem is to limit the alue of u b i a during the test, and tins has been suggested (2, 3, 4). Howeer, some means of predict ing u b i a for a gien soil and strain rate is necessary to incorporate u b ia limits into the rate selection process. Furthermore, because u b ia is not constant during the CRS test, it appears that a critical alue of u b ia must be expressed as a function cif a '. PARAMETERS AFFECTNG u b i a, The way in winch strain rate affects CRS consolidation test results, specifically CR, P c ' and C, and the ability of u b ia to sere as an indicator of when results may be considered reasonable has been shown. Sufficient data exist to establish the relationship between strain rate and u b ia for the particular kaolinite soil used in the tests herein. To extend tins relationship to coer a wide range of soils, the relationship must be expressed in terms of the parameters to which it is most sensitie / /.2.4 / /.6 o.a 1. Figure 11. Comparison of <;, from Linear and Nonlinear Theory (after Wissa (2)). The parameters which most affect u b i a are initial degree of saturation, S, coefficient of consolidation, Cy, and initial height, H. H is a soil-independent parameter. Theoretically, u b ia should decrease as a function of the decrease in H to the i2 power.,75,6 LEGEND TEST NO STRAN RATE Pc %/MN TSF MPa OG b )( <> , VERTCAL EFFECTVE STRESS, 2 4 G (TSF l (MPa) Figure 12. u b ia ' ersus a ' from CRS Tests on Vac-Aire Extruded Specimens. 9

15 J:-!.15.2 f- VERTCAL EFFECTVE STRESS, U / LEGEND '><, "-"'..:.. TEST NO. STRAN RATE s GfG MN % X Po TSF MPa.! (MPA) 4 6 OO(TSF) u--: w "' " ' :> ' " LEGEND U N N TEST NO STRAN RATE s Po,o;t %/MN % TSF " r9 1.2 e.o!!2 X ' "' (.) q w w u VERTCAL EFFECTVE STRESS, U.j MPo OO(TSF) (MPal.25.2 TEST NO X29 LEGEND STRAN RATE %/MN s Po % TSF MPo as.9 b ':c.15 :.1.5 ol-.---l--l---l-l-llll OO(TSF) (tjpal VER TCAL EFFECTVE STRESS,U/ Figure 13. Results of CRS Tests on Partially-Saturated Kaolinite.

16 nitial height was not aried in the testing program and was not considered as a ariable in the deelopment of strain-rate selection criteria. All tests were performed on specimens 25.4 mm (1. inch) high. lfh reduction is used as a method of reducing u b, a minimum of H of.5 inch (12.7 mm) and a minimum diameter to height ratio of 2.5 should be maintained. S and C are soil-dependent and will be used in the deelopment of strain-rate selection criteria. A general discussion of their effect on u / u follows. b By defmition, 9 in which k = permeability and 'Y = unit weight of w water. Therefore, the term C couples permeability with compressibility, two properties which goern the rate of consolidation. The hlgher the permeability, the faster the soil will consolidate; the higher the compressibility, the slower it will consolidate. When the soil is loaded at a constant rate of strain, the hlgher the permeability the slower the pore pressure will rise; the hlgher the compressibility, the faster it will rise. The modified Teraghi model shown in Figure 8 is helpful in isualiing this pore-pressure response. The term u /a is, therefore, inersely proportional to C. b The fact that the parameter C alone is sufficient to describe the consolidation rate process reeals that it is the single most important parameter in determining u /u for a gien strain rate. b Before considering S as a parameter which affects u /u, it should be noted that complete saturation of b the soil, S = 1 percent, is a basic and necessary assumption in all consolidation theories. This, together with the difficulty in determining the effectie stress in partially saturated soils, should eliminate consideration of soils not completely saturated. Howeer, many partially saturated soils exist and are tested in practice. Such test results hae been used successfully. Therefore, although it is somewhat of a contradiction, the effect of the parameters on u b /u must be studied. CRS test results for the partially-saturated remolded specimens preiously described are shown in Figure 13. The plots of u b /u ersus uy' for these tests show increasing u b with increasing S. AsS increases, in the different tests, the alue of u at which u b begins to build up decreases. As the initial degree of saturation decreases, an increasingly greater amount of compression is needed to force any entrapped air into solution. The aerage pore pressure will rise ery slowly until the pore water flows into and fills the oids. Data from the CRS tests shown in Figure 13 will be used later in this report to incorporate the effect of S into the strain-rate selection process. t was stated earlier that the critical alue of fl b must be expressed as a function of ay'. Study of the parameters affecting u b implies ihat u b should be limited at all alues of a aboe P c The low compressibility below P c and, in some cases, the effect of partial saturation inhlbit pore-pressure buildup. Thls can lead to erratic alues of u b / a below P c These alues will, therefore, be discounted. Deelopment of the Strain-Rate Selection Procedure DEVELOPMEN T OF THE RELATONSDP BETWEEN r, C, AND ub/a Four ariables will be considered in the deelopment of a strain-rate selection procedure: r, C, u /a, b and S. At this step in the deelopment, S is not included and, for that reason, all data are from tests on saturated soils. The ariables r, C and u /a will be b related in a way that describes both the CRS tests on kaolinite, presented herein, and the CRS tests on soil types presented elsewhere (J). All alues of u b, reported in this deelopment, are the maximum alues of u /a b within the range of effectie stress aboe P c The relationship between r and u /a for the b kaolinite is shown graphlcally in Figure 14. Theoretically, u b /a should equal ero for a ero strain rate and increase as the strain rate is increased. A maximum u / a b of one is finally approached as r becomes ery large. The alue of u /a from Test No. b 23 did not fit this trend because the high strain rate caused a shlft in the stress-strain cure which raised P changing the c selection point for maximum u /u b. This test was discounted. The general shape of the remaining points o., o. ".5.4, >,,, X >.,.> -.22 r/c,. "n/it, 1_ o--oo,--oo,--o.o,--o.,.ow--o.,---o'w' STRAN RATE (%/MN) Figure 14. Relationship b etween Strain Rate and u b from CRS Tests on Vac-Aire Extruded Specimens. 11

17 ' and the boundary conditions for the u b /a ersus-r relationship may be expressed by an equation of the form y 1 in which y and x are the ordinate and abscissa. An equation of this form was fit to alid CRS test data. The final form of the equation, which best described remolded kaolinite beha ior and undisturbed soil sample beha ior, was in which r is expressed in percent per minute and C is expressed in inches per minute. Equation 11 is shown in Figure 14 for the kaolinite {C =.2 in.2 / min {13 mm 2 /min)) and is used to predict u b /a for tests on undisturbed specimens in Table 4. Equation 11 is sol ed in graphical form, for the ariable C, in Figure 15. This chart may be used to select strain rate for saturated soils if C is known prior to testing. The dashed lines on the chart illustrate the procedure. To use the chart in this way, a maxhnum allowable alue of ub /a must also be selected; u b /a =.3 was arbitrarily chosen for the example shown on the chart. STRAN-RATE SELECTON GUDELNES The selection of the maxhnum alue of u b /a is an important step in the strain-rate selection process. f the u b /a limit is set too low, strain rates will be chosen which are too low to generate any significant pore pressure in the specimen) thereby rendering Equation 4, for C, meaningless. n addition, a low u b /a limit will add significantly to the time required to complete a test. f the u b /a limit is set too high, the consequences already outlined will pre ail. Based on the following obser ations, a limiting alue of u b / a equal to.2 seems reasonable: 11 (1) The pore pressure gradient was established within a reasonable length of time for the CRS test on kaolinite at this limit. (2) The maxhnum theoretical error in C, due to an error in the stressstrain relationship assumption, is approxhnately 12 percent. {3) The CRS test on kaolinite at this lhnit produced stress-strain data in agreement with incrementalload tests and was completed within 32 hours. By limiting the alue of u b /a to less than.2 in the effecti e stress range abo e P C ' u b / a was eliminated as a ariable in the strain-rate selection process. The strain-rate selection process for saturated soils was reduced to a function of C only. Howe er, C usually is not known or not easily determined prior to testing. An indirect method of determining C that has met with some success is a w!;; ---< n.oor l---,''--c,l..--,-"--, -f--,,l..l_ L...:_.,_.w_... -} '.w_. w_u..u.u.,._-'-'-' '-' -l'-l.j-''-'-'-!' (N-2/Mir.!).1.Q. 1 1Mr.t2/SEC COEFFCENT OF CONSOLDATON, C y Figure 15. Strain-Rate Selection Chart for Saturated Soils Based on C and u b. TABLE 4. PREDCTON OF ubfa FOR CRS TESTS ON UNDSTURBED SPECMENS USNG EQUATON 11 c Strain CRS Test Rate Predicted Actual No. (ml11 2 ;sec) (in. 2 /min) (%/min) u b /a u b fa CRS O.Dl5.5.7 CRS CRS CRS KY

18 TABLE 5. ADJUSTED STRAN RATES FOR SATURATED SOLS c CRS Test No. (mm 2 /sec) (in. 2 /min) CRS CRS CRS-18 O.D7.7 CRS KY Actual Predicted Strain Strain Liquid Rate Rate 1 Limit (%/min) (%/min) (%) O.Dl The strain rate necessary, as predicted by Equation 12, to produce a alue of u b /o equal to 2 percent. correlation of liquid limit, LL, and C. An approximate straight-line relationship between liquid llmit and the logarithm of C has been shown (9, 1). Based on this premise, liquid limit was substituted for C in the strain-rate selection chart (Figure 15). CRS test results from the saturated specimens shown in Table 5 were used to generate the relationship between the strain rate required to produce u b / o equal to.2 and liquid limit. Because the CRS tests did not all produce a maximum u b / o of.2 in the effectie stress range aboe P C ' Equation 11 was rearranged to calculate the rate necessary to produce u b /o equal to.2, based on the alue of C measured in the test: r -C ln (1.2)/ The results of Equation 12 are shown as predicted strain rate in Table 5. The predicted strain rates are shown as a function of liquid limit in Figure 16. An arithmetic scale was used for liquid limit, replacing the logarithmic scale for C used in the preious strain-rate selection chart. The data should approximate a straight line when plotted to these scales. A reasonable straightline representation of the data is shown on the figure. This chart forms the strain-rate selection criteria for saturated soils. The final step in the deelopment of the strain-rate selection chart was the correction for partially saturated soils. Data for partially-saturated remolded kaolinite, shown in Figure 13, were used to deelop criteria for partially-saturated soils. The approach was similar to that for saturated soils. The strain rate used in these tests did not produce a u b /o of.2 as required in the selection criteria. For this reason, the actual strain rates in these tests were used to calculate the rate required to produce u b /o equal to.2. This adjustment was based on solutions to Equation 11 for the actual maximum alue of u b / o aboe P c and for the alue of u b /o equal to.2 yielding ' r.2 ; ' '. '.ooo' ' ' r actual ln (1 -.2)! " '1 6 so 1 LQUD LMT("o) 13 : : " Figure 16. Strain-Rate Selection Criteria for Saturated Soils. 13

19 = in which r.2 the adjusted strain rate required to produce u b equal to.2, r actual the actual strain rate in the CRS test, and u b /oy(actual) = the actual maximum alue of llbio in the effectie stress range aboe P c Values of r.2 were plotted ersus the liquid limit of koalinite on the strain-rate selection chart in Figure 17. Assuming that the same straight-line relationship applies to partially saturated soils as applies to the saturated soils, lines parallel to the line for saturated soils were drawn through the points for partially saturated soil in Figure 17. To quantify the relationship between S and strain rate, the perpendicular distance between the parallel lines was plotted ersus - S in Figure 18. The equation describing the best straight-line fit to the data was y 1.82 X, 14 = in which y the perpendicular distance from the 1-percent saturation line and x 1 - Sin percent. Gien thls function, lines may be drawn for any initial 5 4 degree of saturation. This was done for arious alues of Sin Figure 19. Finally, an arbitrary maximum strain rate of.5 percent per minute was established; this permits com- t 3 "' y Y"". 8 2 X o "----'-----'----'----'---...J PERPENDCULAR DSTANCE FROM 1 % SATURATON L1 NE Figure 18. RelationShip between nitial Degree of Saturation and Perpendicular Distance b etween Lines on the Strain-Rate Selection Chari:. X 2..; " r t..; " " r ".1 '---'---:'c_j_.l L_j_:-'-c:':--L_J,--'-...L-l._Jl 2 4 Go ao LQUD LMT{%) Figure 17: Strain Rate Selection Criteria Adjusted for Partially Saturated Soils..ooo1 '---'---c,l _1 -,c'c, ---''-- f6c-'--..,o-,-l_l""''c-'--!,l.o,-'--,l,., LQUD LMT (%) Figure 19. Strain-Rate Selection Chart. 14

20 pletion of a CRS test within approximately one working day. When strain rates near or aboe the maximum are used, transient conditions described by Wissa (2) should be expected. Figure 19 allows the pre-selection of strain rate for CRS tests based on liquid limit and initial degree of saturation. As mentioned preiously, considerable latitude exists in the choice of a proper strain rate; therefore, the alue gien by the chart form guidelines for the strain-rate selection process. Conclusions 1. The appropriate rate of strain in the CRS consolidation test is one which will limit the alue of u b to less than.2 in the effectie stress range aboe P c. 2. Some latitude exists in the selection of an appropriate strain rate. 3. The general range of appropriate strain rates for CRS consolidation testing is.1 to.5 percent per minute. 4. f the alue of C for a particular saturated soil is known prior to testing, Figure 15 can be used to select the rate of strain. 5. f the alue of C for a particular soil is not known prior to testing, or if the soil is partialiy saturated, Figure 19 can be used to select the rate of strain based on the liquid limit and the initial degree of saturation. Summary A schema based on theoretical considerations and experimental data has been proposed for strainrate selection in the CRS consolidation test. The strain-rate selection chart presented in Figure 19 not only establishes numerical guidelines but, more importantly, establishes a framework for strain-rate selection techniques based on the more important ariables in the CRS test. As the CRS consolidation test becomes more widely used, the strain-rate selection chart may be modified based on new data that will be generated. This approach, together with sound engineering judgment, should eliminate the uncertainty in the strainrate selection process. References 1. Hamilton, J. J.; and Crawford, C. V.;mproed Detennination of Preconsolidation Pressure of a Sensitie Clay, Special Technical Publication No. 254, ASTM, Philadelphia, Wissa, A. E. Z.; Christian, J. T.; Dais, E. H.; and Heiberg, S.; Consolidation at Constant Rate of Strain, Journal of the Soil Mechanics and Foundations Diision, ASCE, Vol 97, No. SMO, New York, October Gorman, C. T.; Constant-Rate-ofStrain and Controlled-Gradient Consolidation Testing, Research Report No. 448, Diision of Research, Kentucky Department of Transportation, Lexington, May Smith R. E.; and Wahls, H. E.; Consolidation under Constant Rates of Strain, Journal of the Soil Mechanics and Foundations Diision, ASCE, Vol 95, No. SM2, New York, March Chan, C. K.; Low-Friction Seal System, Journal of the Geotechnical Engineering Diision, ASCE, VallO!, No. GT9, New York, September Crawford, C. B.; nterpretation of the Consolidation Test, Journal of the Soil Mechanics and Foundations Diision, ASCE, Vol 9, No. SM5, New York, September Salifors, G.; Preconsolidation Pressure of Soft, High Plastic Clays, Thesis presented to Chalmers Uniersity of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy, October Lowe, J.; New Concepts in Consolidation and Settlement Analysis, Journal of the Geotechnical Engineering Diision, ASCE, Vol 1, No. GT6, New York, June Teraghi, K.; and Peck, R. B.; Soil Mechanics 15

21 in Engineering Practice, John Wiley and Sons, Somerset, NJ, Design Manual - Soil Mechanics, Foundations, and Earth Structures, NAVFAC DM-7, Department of the Nay, aal Facilities Engineering Command, Washington, DC, March,